相关论文: A classification of the dynamics of three-dimensio…
We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution…
The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to…
We study the observable long-term behavior of typical continuous dynamical systems on the interval $[0,1]$. For a residual subset of $C([0,1])$, the Milnor, statistical, and physical (in the sense of Ilyashenko) attractors coincide and are…
Predators often consume multiple prey and by mutually subsidizing a shared predator, the prey may reciprocally harm each other. When predation levels are high, this apparent competition can culminate in a prey species being displaced.…
We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium…
Intrinsically noisy mechanisms drive most physical, biological and economic phenomena, from stock pricing to phenotypic variability. Frequently, the system's state influences the driving noise intensity, as, for example, the actual value of…
Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and…
We develop a landscape-flux framework to investigate observed frequency distributions of vegetation and the stability of these ecological systems under fluctuations. The frequency distributions can characterize the population-potential…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and nonliving matter. Group interactions are a particularly important and widespread class,…
We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population…
State-space models are dynamical systems defined by a latent and an observed process. In ecology, stochastic state-space models in discrete time are most often used to describe the imperfectly observed dynamics of population sizes or animal…
We analyse the asymptotic behaviour of integro-differential equations modelling $N$ populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total…
We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species…
Numerical continuation methods for deterministic dynamical systems have been one of the most successful tools in applied dynamical systems theory. Continuation techniques have been employed in all branches of the natural sciences as well as…